A semicircular garden bed at the botanical gardens needs to be fenced off while the seedlings are established. If the straight edge of the bed is 20.5m in length, calculate the total length of fencing needed to surround the garden bed.
So you need the length of the straigh edge, which you know is 20.5 m, plus the semicircle's perimeter.
The radius is 10.25
So fence = 20.5 + π(diameter)
= 20.5 + 20.5π
= ...
thanks
D = 20.5 m. = diameter.
L = D + pi*D/2 = 20+(3.14*20.5/2) = 52.2 m.
To calculate the total length of fencing needed to surround the semicircular garden bed, we need to find the perimeter of the garden bed.
The perimeter of any shape can be calculated by adding the lengths of all its sides.
In this case, the garden bed is a semicircle, so it has a curved edge (the circumference of the semicircle) and a straight edge.
The curved edge is half the circumference of a circle. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Since we have the straight edge length (20.5m), we can find the radius by dividing the straight edge length by π (approximately 3.14) and then dividing by 2 because we only need half the circumference.
Radius = Straight Edge Length / (2π)
Radius = 20.5 / (2 * 3.14) ≈ 3.26m
Now, we can calculate the circumference using the formula C = 2πr.
Circumference = 2π * Radius
Circumference = 2 * 3.14 * 3.26 ≈ 20.48m
Finally, to find the total length of fencing needed, we add the straight edge length and the circumference.
Total Length of Fencing = Straight Edge Length + Circumference
Total Length of Fencing = 20.5 + 20.48 ≈ 40.98m
Therefore, the total length of fencing needed to surround the garden bed is approximately 40.98 meters.